There are 43 trophies that can be collected.

Bronze

I'm the Man on the Mountain, come on up
All Tournament Mode cup events completed

W – is for Winner
Placed 1st in all the Events completed within a single Zone.

Home is where the Heart is
Game completed with Kelly

Till Death do us Part
Game completed with Reggie

Shred some Faces
Game completed with Bedlam

Who's the Cat that won't cop out
Game completed with Superstar

Phantom of the Opera
Game completed with Nazar

Ode to Mother Russia
Game completed with Natalya

Into the Sunset
Game completed with Jackson

Go out for a Pass
Game completed with Brock

Glove Slapped
All Challenge Mode Events completed

Zombie Community Culling
Rack up a 50+ Zombie Killing Spree

Flesh Hacky Sack
Hit a Shambler into the air, then kill it before it lands

Death by Goldberg Machine
Crush upwards of 5 Zombies by knocking a solid prop into them

Undeath From Above
Crush 10 Zombies by way of air landing over the course of any event

Driving Miss Zombie
Carry a roof perched Leaper over 1 jump, activating Jump-Cam

Crash & Burn
Multiplayer: Kill another human player while both your vehicles are airborne

Survivalist
Multiplayer: Survive an entire event without dying once.

Wastelander
Multiplayer: Complete in 100 online events.

Variety is the Spice of Life
Wreck all vehicles in an event at least once each

Bully
Wreck the designated Rival 5 times in one event

Donut King
Completed uninterrupted donuts for 10 seconds

He's a Wreckin' Machine!
Wreck 5 vehicles during one Juggernaut or Damage Fever Rage

The Blind leading the Blinded
Wreck 5 vehicles during one Flashbling or Cloak Rage

Keep Back: Highly Volatile
Wreck 3 vehicles with one Shockwave or Gross Polluter Rage

From the Heavens
Wreck 3 vehicles with one Surgical Strike or Gravity Well Rage

Silver

And we'll keep on fighting till the end
Blood Drive Championship Cup Completed

C – is for Champion
Place 1st in all events in the Blood Drive tournament

Hardcore Strip teased
Hardcore Cup completed with Kelly

Hardcore Cup Flatlined
Hardcore Cup completed with Reggie

Hardcore Cup Rolled
Hardcore Cup completed with Bedlam

Hardcore Cup Body slammed
Hardcore Cup completed with Superstar

Hardcore Cup Assassinated
Hardcore Cup completed with Nazar

Hardcore Cup Conquered
Hardcore Cup completed with Natalya

Hardcore Cup Lynched
Hardcore Cup completed with Jackson

Hardcore Cup Sacked
Hardcore Cup completed with Brock

Zombie Populace Culling
Rack up a 100+ Zombie Killing Spree

God Save the King
Multiplayer: Player collected and kept King of the Hill status for the entire Event duration, without divestment

Untouchable
Multiplayer: Player survived the entire Hot Potato Event duration without receiving the Jackpot Bomb once

4 Secret

http://www.ps3trophies.org/game/blood-drive/trophies/